Strongly quasipositive knots are concordant to infinitely many strongly quasipositive knots

Paula Truöl (ETH Zurich)

16-Dec-2022, 16:00-17:15 (15 months ago)

Abstract: Knots are smooth embeddings of the (oriented) circle S^1 into the 3-sphere S^3, usually studied up to an equivalence relation called ambient isotopy. A natural generalization in dimension 4 of the question whether certain knots are isotopic to the trivial knot is the concept of concordance, another equivalence relation on the set of knots. We show that every non-trivial strongly quasipositive knot is (smoothly) concordant to infinitely many pairwise non-isotopic strongly quasipositive knots. In contrast to our result, it was conjectured by Baker that concordant strongly quasipositive fibered knots are isotopic. Our construction uses a satellite operation whose companion is a slice knot with maximal Thurston-Bennequin number -1. In the talk, we will define the relevant terms necessary to understand the theorem in the title, and explain the context of this result. If time permits, we will say a few words about how the construction extends to links.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic


CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

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Organizers: Julien Keller*, Duncan McCoy
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